scholarly journals Point-splitting method of the commutator anomaly of Gauss law operators

1997 ◽  
Vol 56 (4) ◽  
pp. 2236-2241 ◽  
Author(s):  
R. A. Bertlmann ◽  
Tomáš Sýkora
Keyword(s):  
Splitting Method ◽  
Point Splitting

The constraint equation of the vertex function of quantum anomaly and Dyson–Schwinger equations in massless QED2 theory

2020 ◽  
Vol 35 (18) ◽  
pp. 2050146
Author(s):  
Yang Yu ◽  
Jian-Feng Li
Keyword(s):  
Vertex Function ◽  
Axial Vector ◽  
Splitting Method ◽  
Vector Current ◽  
Constraint Equation ◽  
Axial Vector Current ◽  
Fermion Propagator ◽  
Schwinger Model ◽  
Quantum Anomaly ◽  
Point Splitting

In this paper, we calculate the quantum anomaly for the longitudinal and the transverse Ward–Takahashi (WT) identities for vector and axial-vector currents in QED2 theory by means of the point-splitting method. It is found that the longitudinal WT identity for vector current and transverse WT identity for axial-vector current have no anomaly while the longitudinal WT identity for axial-vector current and the transverse WT identity for vector current have anomaly in QED2 theory. Moreover, we study the four WT identities in massless QED2 theory and get the result that the four WT identities together give the constraint equation of the vertex function of quantum anomaly. At last, we discuss the Dyson–Schwinger equations in massless QED2 theory. It is found that the vertex function of the quantum anomaly has corrections for the fermion propagator and Schwinger model.

POINT-SPLITTING REGULARIZATION IN N=2 SUPERCONFORMAL FIELD THEORY

1999 ◽  
Vol 14 (20) ◽  
pp. 3207-3237
Author(s):  
BELAL E. BAAQUIE ◽  
KOK KEAN YIM
Keyword(s):  
Field Theory ◽  
Complex Structure ◽  
Splitting Method ◽  
Superconformal Algebra ◽  
Operator Product ◽  
Central Extensions ◽  
Superconformal Field Theory ◽  
Conformal Field ◽  
Coset Model ◽  
Point Splitting

In this paper, the method of point-splitting regularization is applied on the N=2 superconformal field theory, specifically the superconformal coset model formulated by Kazama and Suzuki. We obtain the correct central extensions for the N=2 superconformal algebra after many nontrivial cancellations among the various singular expressions. This shows the consistency of the point-splitting method in an N=2 superconformal system. In the process, we arrive at the Kazama–Suzuki conditions which govern the existence of an N=2 superconformal coset model in the N=1 coset model. In addition, we obtain a number of mathematical relations between the structure constants and the complex structure of the model, which allow us to simplify the U(1) current of the N=2 superconformal algebra. In the course of our analysis, we found that, at least in a two dimension conformal field theory, the operator product expansion of a composite current must be written in a way which conveys all the information of the commutator equations.

POINT-SPLITTING REGULARIZATION IN (SUPER)CONFORMAL FIELD THEORY

1999 ◽  
Vol 14 (18) ◽  
pp. 2887-2904
Author(s):  
BELAL E. BAAQUIE ◽  
KOK KEAN YIM
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Splitting Method ◽  
Central Extensions ◽  
Singular Terms ◽  
Superconformal Field Theory ◽  
Conformal Field ◽  
Point Splitting ◽  
Super Conformal Field Theory ◽  
Wick’S Theorem

The method of point-splitting regularization is applied on the two-dimensional (super)conformal field theory. This method is first used to regularize the fermionic conformal field theory and then the N=1 superconformal field theory. We obtain the correct central extensions for the conformal algebra and the N=1 superconformal algebra. We arrived at these results only after some nontrivial, but exact, cancelations among all the singular terms, as required by the consistency of the point-splitting method. In the course of our analysis, we rederive Wick's Theorem directly from the commutation equations of the fundamental fields.

HAMILTONIAN FORMULATION OF CHIRAL SCHWINGER MODEL IN FOUR DIMENSIONS

1989 ◽  
Vol 04 (26) ◽  
pp. 2531-2537
Author(s):  
W.T. KIM ◽  
B.H. CHO ◽  
D.K. PARK
Keyword(s):  
Splitting Method ◽  
Hamiltonian Formulation ◽  
Four Dimensions ◽  
Schwinger Model ◽  
Schrödinger Representation ◽  
Point Splitting

The four dimensional chiral Schwinger model can be quantized through the generalized point splitting method in Schrödinger representation. It satisfies the consistency and unitarity in the physical subspace.

scholarly journals A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

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